@article{AIHPA_1994__61_2_189_0, author = {Dimassi, Mouez}, title = {D\'eveloppements asymptotiques pour des perturbations fortes de l'op\'erateur de {Schr\"odinger} p\'eriodique}, journal = {Annales de l'I.H.P. Physique th\'eorique}, pages = {189--204}, publisher = {Gauthier-Villars}, volume = {61}, number = {2}, year = {1994}, mrnumber = {1311064}, zbl = {0827.35091}, language = {fr}, url = {http://www.numdam.org/item/AIHPA_1994__61_2_189_0/} }
TY - JOUR AU - Dimassi, Mouez TI - Développements asymptotiques pour des perturbations fortes de l'opérateur de Schrödinger périodique JO - Annales de l'I.H.P. Physique théorique PY - 1994 SP - 189 EP - 204 VL - 61 IS - 2 PB - Gauthier-Villars UR - http://www.numdam.org/item/AIHPA_1994__61_2_189_0/ LA - fr ID - AIHPA_1994__61_2_189_0 ER -
%0 Journal Article %A Dimassi, Mouez %T Développements asymptotiques pour des perturbations fortes de l'opérateur de Schrödinger périodique %J Annales de l'I.H.P. Physique théorique %D 1994 %P 189-204 %V 61 %N 2 %I Gauthier-Villars %U http://www.numdam.org/item/AIHPA_1994__61_2_189_0/ %G fr %F AIHPA_1994__61_2_189_0
Dimassi, Mouez. Développements asymptotiques pour des perturbations fortes de l'opérateur de Schrödinger périodique. Annales de l'I.H.P. Physique théorique, Tome 61 (1994) no. 2, pp. 189-204. http://www.numdam.org/item/AIHPA_1994__61_2_189_0/
[A-D-H] Eigenvalue branches of the Schrödinger operators H - λω in a gap of σ (H), Comm. Math. Phys., Vol. 121, 1989, pp. 291-321. | MR | Zbl
, , ,[Bi] Discret spectrum in the gap of the continuous one in the large coupling limit, Oper. Theory: Adv. Appl., Vol. 46, 1990, pp. 17-25.[2] The discret spectrum in a gap of the perturbed periodic operator at large coupling constants, Proc. Conf. Rigorous Results in Quantum Dynamics, Liblice Castle, June 11-15, 1990 (to appear).[3] On discret spectrum in gaps of a perturbed periodic second order operator, Funktional Anal i Prilozken (to appear). | MR
: [1][B-S] Estimates for the singular numbers of integral operators, Uspekhi Mat. Nank., Vol. 32, 1977, pp. 17-84,English trans. in Russian Math. Surveys, Vol. 32, 1977, pp. 15-89.[2] Asymptotic behaviour of the spectrum of pseudo-differential operators with anisotropically homogeneous symbols, I, Vestnik Leningrad Uni. Math. Mekh. Astronom., 1977, n° 13, pp. 3-21; II, 1989, n° 3, 5, 10; English trans. in Vestnik Leningrad Univ. Math., Vol. 10, 1982; Vol. 12, 1980.[3] Negative discret spectrum of the Schrödinger operator with large coupling constant: a qualitative discussion, Ope. Theory: Adv. App., Vol. 46, 1990, pp. 3-16.[4] Schrôdinger operator. Estimates for the number of the bound states as a function-theoretic problem, Lectures of the XIV School on operator theory and Funciton Spaces, I, Novgorod, 1990; English trans., Amer. Math. Soc., Providence RI (to appear).[5] Estimates for the number of negative eigenvalues of the Schrödinger operator and its generalizations, Advances in Soviet Mathematics, Vol. 7, 1991. | MR
and : [1][D-H] On the existence of eigenvalue of the Schrödinger operator (H - λW) in a spectral gap of, Comm. Math. Phys., Vol. 103, 1986, pp. 461-490. | MR | Zbl
and ,[Di] Développements asymptotiques des perturbations lentes de l'opérateur de Schrôdinger périodique, à paraître dans Comm. in P.D.E., 1993. | Zbl
,[G-S] On a theorem of Deift and Hempel, Comm. Math. Phys., Vol. 118, 1988, pp. 597-634. | MR
, ,[He-Sj] Équation de Schrödinger avec champ magnétique fort et équation de Harper, Preprint Juin 1988.
, ,[H] On the asymptotic distribution of the eigenvalue branches of a Schrödinger operator (H - λW) in a spectral gap of H, J. Reine Angew. Math., Vol. 399, 1989, pp. 38-59. | MR | Zbl
,[K-M] On the density of states of Schrödinger operators with a random potential, J. Phys. A. Math. Gen., Vol. 15, 1982, pp. 2139-2156. | MR | Zbl
, ,[Re-Si] Methods of modern mathematical physics, I-IV, Academic Press, pp. 1974-1979. | MR
, ,[Sh] The spectral theory and the index of elliptic operators with almost periodic-coefficients, Russian Math. Surveys, Vol. 34, 1979, pp. 109-157. | MR | Zbl
,[Sj] Microlocal analysis for the periodic magnetic Schrôdinger equation and related questions, Lectures Notes in Mathematics, Vol. 1495, 1989, pp. 237- 332. | MR | Zbl
,[So] Weyl asymptotics for the discret spectrum of the perturbed Hill operator, Advances in Soviet Mathematics, Vol. 7, 1991, pp. 159-178. | MR | Zbl
,